How to define perimeter and calculate it for squares, rectangles, and circles.
How to prove that an angle inscribed in a semicircle is a right angle; how to solve for arcs and angles formed by a chord drawn to a point of tangency.
How to derive the formula to calculate the area of a sector in a circle.
How to define the apothem and center of a polygon; how to divide a regular polygon into congruent triangles.
How to graph the special cases of the family r = a + b cos (theta) when a or b = 0.
How to use the unit circle to derive the tangent identity and the Pythagorean identity.
How to calculate the circumference of a circle.
How to use the unit circle to derive identities that are useful in graphing the reciprocal trigonometric functions.
How to prove the surface area of a cylinder formula.
How to graph y = tan(theta) for 0 <= theta < pi/2.
How we define sine and cosine for all angle measures using the unit circle.
How to derive the formula for the area of an annulus.
How to calculate the surface area of any cone explaining lateral surface area.
How to calculate the surface area of a cylinder joined to a cone.
How to compare the volume of a cone and a cylinder and how to calculate the volume of a cone given the radius and height.
How to define the reciprocal trigonometric functions, the reciprocal identities, and the Pythagorean identities.